Titlebook: Convex Analysis for Optimization; A Unified Approach Jan Brinkhuis Textbook 2020 Springer Nature Switzerland AG 2020 Convex set.Convex func

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Textbook 2020bjects in a precise yet light-minded spirit... For experts in the field, this book not only offers a unifying view, but also opens a door to new discoveries in convexity and optimization...perfectly suited for classroom teaching.."  .Shuzhong Zhang., Professor of Industrial and Systems Engineering,

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Convex Sets: Binary Operations,and the inverse sum. The defining formulas for these binary operations look completely different, but they can all be generated in exactly the same systematic way by a reduction to convex cones (‘homogenization’). These binary operations preserve closedness for polyhedral sets but not for arbitrary

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Convex Sets: Topological Properties,ame ‘shape’, whether . is bounded or unbounded: it is a slightly deformed open ball (its relative interior) that is surrounded on all sides by a ‘peel’ (its relative boundary with its points at infinity adjoined). In particular, this is essentially a reduction of unbounded convex sets to the simpler

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Convex Sets: Dual Description, a novel proof is given: this amounts to just throwing a small ball against a convex set. Many equivalent versions of the duality result are given: the supporting hyperplane theorem, the separation theorems, the theorem of Hahn–Banach, the fact that a duality operator on convex sets containing the o

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Convex Functions: Dual Description,one has a rule of the type . where ⊙ is another one of the eight binary operations on convex functions. Again, homogenization generates a unified proof for these eight rules. This requires the construction of the conjugate function operator by means of a duality operator for convex cones (the polar

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